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Unformatted text preview: PADP 8670 Fall 201 l
Fertig UGA Homework 5 Solutions 1. The demand function for cigars is PrZKlOZQ and the supply function is P=3+Q,
where P is the price per box and Q is the number ofboxes. Cigars are taxed at $4 per
box. a. Draw the supply and demand before and after the tax is imposed, indicating
with actual numbers the quantities and prices before and after the tax. S=D: 2402Q=3+Q
23723Q Z430
P=3+79 Zap P=82 Before tax: P After tax: git—.57
New demand: 8
Pz2362Q 
236—2Q=3+Q 302/3
233=3Q 0:77.67 ,5 _ ‘
P s =3+77.67 "
P s =80.67 777; 7&l l20 61
P d 280.6744
P d =84.67
b. Do consumers and suppliers share the cost ofthe tax equally? Ifnot, what
share do they each pay? No. Consumers pay $84.67~$82=$2.67 ofthe $4 tax: about 67%
Producers pay $82$80.67=$1.33 of the $4 tax: about c. Given your answer to [a], is the price elasticity of demand elastic or inelastic? Since consumers pay more of the tax, the price elasticity of demand is .
Producers pass on a lot ofthe tax to consumers because they know consumers are not very price sensitive. 2. Assume that the demand for bread is Q=454P and the supply of bread is Qx15+8P,
Where P is the price ofa loafand Q is the number ofloaves of bread. Assume that
the government wants to ensure that the price of bread never rose above $2 per
loaf. The policy proposed is to pay bakers enough ofa subsidy for each loafofbread
so that the price is $2 per loaf. How much would the subsidy per loafhave to be?
Make sure to draw a graph ofthe supply and demand before and after the subsidy is
given, indicating with actual numbers the quantities and prices before and after the subsidy. Demand: P
Q=4—54P 4P=45Q ll 1”:
P:11.25 — Q/4 Supply:
Q=15+8 8P=Q15
P:1.875+Q/8 U! ”all; \
454P=15+8P 2.75 _ S w/subswlﬁ
30:1 P 25 '.
P=2.5 Z
Q:454*2.5 IfP=$2. then 16%: ” $76 Q d =454*2 “7995 To figure out subsidy amount, what price would suppliers need to supply 37 units?
37:15+8P 22=8P P=2.75 So, subsidy must be $2.75~$2. Alternate approach: To figure out subsidy amount, figure out what new supply curve
intercept would be to get an intersection of the new supply curve and the demand
curve at $2 and 37 loaves. New supply curve: P=1.8’75+s+Q/8 Demand curve: P=11.25Q/4— 52D, plug in Q=37 and solve for s: 1.875+s+37/8=11.2537/4 s=11.259.25+1.8754.625 ...
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 Fall '10
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